Investigation of Minkowski Patch Antenna with Meander Line Split Ring Resonator (ML-SRR) Structure.
2013 7th European Conference on Antennas and Propagation (EuCAP)
Investigation of Minkowski Patch Antenna with
Meander Line Split Ring Resonator (ML-SRR)
Structure
1
H. Nornikman, 1B. H. Ahmad, 1M. Z. A. Abd Aziz, 2M. K. A. Rahim, 1A. R. Othman
1
Center for Telecommunication Research and Innovation (CeTRI),
Faculty of Electronics and Computer Engineering,
Universiti Teknikal Malaysia Melaka (UTeM), Melaka, Malaysia
2
Faculty of Electrical Engineering,
Universiti Teknologi Malaysia, Johor, Malaysia
nornikman84@yahoo.com, badrulhisham@utem.edu.my, mohamadzoinol@utem.edu.my, mkamal@fke.utm.my,
rani@utem.edu.my
Abstract—The objective of this paper is to investigate the
effect of the meander line split ring resonator on the modified
Minkowski patch antenna. In this work, a modified Minkowski
patch antenna with meander line split ring resonator (ML-SRR)
and quadruple-P shaped split ring resonator (QPS-SRR)
structure is presented. This proposed modified patch antenna
with SRRs structures achieved remarkable 2.644 dB of gain at
the frequency of 2.402 GHz compared to the normal Minkowski
antenna without SRR structures with only 2.348 dB. This
antenna had been simulated in the CST Microwave Studio
simulation software.
that four rectangular or square shape of copper had been cut
from the patch, shown in Figure 1.
(a)
Index Terms—Minkowski antenna, split ring resonator,
metamaterial
I.
(b)
INTRODUCTION
In recent years, there are many works to enhance the gain
performance of the patch antenna design. The metamaterial or
left-handed media (LHM) structure is one of the technique
improve this problem. In 1968, Veselago had been proposed
this technique by implementing split ring resonator (SRR)
structure with metal wires [1]. Many researchers have studied
patch antenna that adds this SRR structure, especially in
wireless local area network (WLAN) range of 2.4 GHz. This
paper had been investigating the effect of the meander line split
ring resonator (ML-SRR) and the quadruple-P shaped split ring
resonator (QPS-SRR) structure of the modified Minkowsi
patch antenna. The parameters that are considered in this work
are return loss, gain, directivity, and the radiation pattern of the
patch antenna [2].
The geometry Fractal methods can include in many types
such as Sierpinski carpet [3], Koch Fractal [4], Minkowski
Fractal [5-6] Hilbert Fractal [7] and 3/2 Curve Fractal [8]. The
Minkowski Fractal antenna is one popular technique to
miniaturize the size of the patch antenna [9]. This Minkowski
Fractal also can affect the multiband of frequency [10].
The Minkowski curve can be characterized by the iteration
factor [11]. Zero iteration is represented by the normal patch
without any scraped out of copper [12]. First iteration show
978-88-907018-3-2/13 ©2013 IEEE
(c)
(d)
Figure 1. Modified Minkowski patch antenna iteration stage ; (a) Zero
iteration; (b) First iteration; (c) Second iteration (d) Third iteration
II.
PROPOSED SRR
Split ring resonators (SRRs) design is used to produce the
negative dielectric constant (permittivity) and negative
permeability [13]. From the previous work, this structure can
increase the gain and miniaturize the size of the patch antenna
and have the capability to improve the gain performance [1415]. This SRR structure also has potential to increase the
reflection loss performance of the pyramidal microwave
absorber [16]. Figure 2 and Table I shows the proposed
meander line split ring resonator (ML-SRR) while Figure 3 and
3233
2013 7th European Conference on Antennas and Propagation (EuCAP)
Table II shows the Quadruple-P shaped split ring resonator
(QPS-SRR). The dimension of the ML-SRR is 8.29 mm x
10.33 mm. The dimension of the larger QPS-SRR is 1.68 mm x
2.49 mm while the dimension of the smaller QPS-SRR is 1.37
mm x 2.03 mm.
A1
III.
PROPOSED ANTENNA
Minkowski Fractal shape based antenna is designed based
on the bigger and smaller size of square shape generator [3].
Figure 4 and Table III shows the modified Minkowski patch
antenna (without SRR structure added). This antenna uses FR4 board substrates with dielectric constant of 4.3, tangent loss
of 0.025, and thickness of 1.6 mm .
Ws
Wp
(a)
(b)
A2
Ls
Lp
Figure 2. Structure unit of meander line split ring resonator (ML-SRR) (a)
normal condition SRR; (b) complimentary SRR condition
TABLE I.
Wf
Lf
DIMENSION OF THE STRUCTURE UNIT OF MEANDER LINE SPLIT
RING RESONATOR (ML-SRR)
Parameter part
Dimension (mm)
A1
A2
8.29
Lc
Wc
Figure 4. Modified Minkowski patch antenna (without SRR structure added)
10.33
TABLE III.
C1
Parameter part
Dimension (mm)
Ws
Ls
34
45
Wp
28.86
Lp
28.86
Wf
0.5
Lf
9.95
Lc
4.55
Wc
2.81
C2
B2
(a)
B1
(b)
Figure 3. Quadruple-P shaped split ring resonator (QPS-SRR); B1 = 1.68
mm, B2 = 1.37 mm, C1 = 2.49 mm, C2 = 2.03 mm (a) normal condition SRR;
(b) complimentary SRR condition
TABLE II.
DIMENSION OF THE MODIFIED MINKOWSKI PATCH ANTENNA
(WITHOUT SRR STRUCTURE ADDED)
DIMENSION OF THE STRUCTURE UNIT OF QUADRUPLE-P
SHAPEDSPLIT RING RESONATOR (QPS-SRR)
Parameter part
Dimension (mm)
B1
B2
1.07
C1
1.68
C2
0.76
1.29
Figure 5 shows the different location of ML-SRR and
QPS-SRR structure of the modified Minkowski patch antenna.
Type A antenna had been representing the attached 4 pair of
ML-SRR and QPS-SRR at the patch antenna to improve the
gain performance. In Type B, a rectangular stripline had been
added to control the location of the resonant frequency of the
antenna.
3234
2013 7th European Conference on Antennas and Propagation (EuCAP)
frequency. The best reflection loss had been shown by second
iteration of the Minkowski patch antenna. This antenna had
been resonating at 2.402 GHz of frequency. The third iteration
shows the worst return loss performance but it had been shifted
from 2.402 GHz to the 2.202 GHz, the different frequency
point of 200 MHz.
Return Loss of Modified Minkowski Patch Antenna with SRR
0
Z1
(b)
-10
Return loss, dB
(a)
-20
-30
Zero Iteration
First Iteration
Second Iteration
Third Iteration
-40
-50
Z3
Z2
2.1
2.3
2.4
2.5
2.6
Frequency, GHz
(d)
(c)
Figure 6. Return loss performance of modified Minkowski patch antenna
with ML-SRR and QPS-SRR (in different iteration stage)
Figure 5. Modified Minkowski patch antenna with different variation ;
(a)Type A; (b) Type B; (c) Type C (d) Type D
For the Type C antenna, a larger version of QPS-SRR
antenna had been added at the center location of patch antenna
to enhance more gain of the antenna. In the Type D, 4 smaller
versions of QPS-SRR had been removed from the design.
Table IV shows the adjustment Stripline length to optimize the
resonant frequency to 2.402 GHz
TABLE IV.
2.2
THE ADDITION OF STRIPLINE TO ADJUST THE FREQUENCY
RANGE TO 2.402 GHZ
Table V shows return loss, resonant frequency and the
bandwidth of the Minkowski patch antenna. It shows that the
second iteration Minkowski patch antenna had been achieved
the best reflection loss with - 47.990 dB at a frequency of
2.402 GHz. The worst return loss performance had been
achieved by third iteration by only - 14.665 dB but it has the
wider bandwidth compared to the other iteration stage. This
antenna (at third iteration stage) has a bandwidth of 100.7
MHz.
Minkowski Antenna type
Rectangular strip
length added (mm)
Without SRR
-
Type A
-
Minkowski
Antenna stage
Resonant
frequency
Return loss
(dB)
Bandwidth
(MHz)
Type B
5.2
Zero iteration
2.312
- 22.680
70.7
Type C
6.8
First iteration
2.392
- 36.925
69.6
Second iteration
2.402
- 47.990
60.8
Type D
6.8
Third iteration
2.202
-14.665
100.7
IV.
TABLE V.
RETURN LOSS PERFORMANCE OF MODIFIED MINKOWSKI
PATCH ANTENNA WITH ML-SRR AND QPS-SRR (IN DIFFERENT ITERATION
STAGE)
RESULT
Figure 6 shows the return loss performance of the modified
Minkowski patch antenna with ML-SRR and QPS-SRR (in
different iteration stage). From the graph, it shows that, the
different type of stage will control where is the resonant
Table VI represents the result of the gain and the directivity
of the antenna (in different iteration stage). The first iteration
shown the best gain performance with 2.495 dB while the
worst gain had been shown by third iteration with only 0.775
dB.
3235
2013 7th European Conference on Antennas and Propagation (EuCAP)
TABLE VI.
GAIN AND DIRECTIVITY PERFORMANCE OF MODIFIED
MINKOWSKI PATCH ANTENNA WITH ML-SRR AND QPS-SRR (IN DIFFERENT
ITERATION STAGE)
Minkowski Antenna
iteration stage
Gain (dB)
Directivity (dBi)
Zero iteration
2.332
5.441
First iteration
2.495
5.505
Second iteration
2.348
5.539
Third iteration
0.775
5.434
patch antenna from the 2.348 dB to 2.644 dB. The addition of
the rectangular stripline had been located back the resonant
frequency from the 2.480 GHz at the Type A to 2.402 GHz in
Type B antenna. This SRR structure did not give the big impact
of the bandwidth performance.
Figure 8 shows the 3D radiation pattern of the modified
Minkowski antenna with SRR structure.Table VIII represents
the gain and directivity performance of the different type of
modified Minkowski patch antenna.
Figure 7 and Table VII shows the resonant frequency,
return loss and bandwidth of the different type of modified
Minkowski patch antenna From the graph, it shows that the
best performance of the return loss is the modified Minkowski
patch antenna (without SRR structure) with – 47.999 dB at
2.402 GHz of frequency.
Return Loss of Different Type of
Modified Minkowski Patch Antenna with SRR
10
0
Return loss, dB
-10
-20
-30
-40
Without SRR
Type A
Type B
Type C
Type D
-50
-60
2.30
2.35
2.40
2.45
2.50
2.55
Frequency, GHz
Figure 7. Return loss performance of the different type of modified
Minkowski patch antenna with ML-SRR and QPS-SRR
TABLE VII.
RETURN LOSS AND BANDWIDTH OF DIFFERENT TYPE OF
MINKOWSKI PATCH ANTENNA WITH SRR
Figure 8. 3D radiation pattern of the antenna
Minkowski
Antenna type
Resonant
frequency
Return loss
(dB)
Bandwidth
(MHz)
Without SRR
2.402
- 47.990
69.8
Type A
2.480
- 33.340
72.3
Directivity (dBi)
2.402
- 38.128
68.1
Minkowski Antenna
type
Gain (dB)
Type B
Type C
2.402
- 31.328
68.7
Without SRR
2.348
5.539
Type D
2.402
- 38.086
71.3
Type A
2.627
5.644
Type B
2.644
5.506
Type C
2.629
5.501
Type D
2.486
5.522
TABLE VIII.
The addition of the SRR structure had been reduced the
return loss performance. The addition of the SRR had been
enhanced the gain of the Minkowski patch antenna. It shows
that in Type B antenna, it increases the gain of the Minkowski
3236
GAIN AND DIRECTIVITY OF DIFFERENT TYPE OF MINKOWSKI
PATCH ANTENNA WITH SRR
2013 7th European Conference on Antennas and Propagation (EuCAP)
V.
CONCLUSION
After simulation done, it shows that the gain had been
enhanced by the addition of the ML-SRR and QPS-SRR on the
modified Minkowski patch antenna. An improvement of the
gain by 0.296 dB from 2.348 dB to 2.644 dB. The SRR has the
capability can control the resonant frequency. The proposed
antenna design can be integrated with RF transmitter [17] and
RF receiver [18] to form a complete WLAN front-end system.
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[B] A. Ismahayati, P. J., Soh, R. Hadibah, G. A. E. Vandenbosch,
Design and Analysis of A Multiband Koch Fractal Monopole Antenna,
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Affendi, L. Mohamed, N. Sudin, A. A. Ali, Complimentary Structure of
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on Applied Electromagnetics (APACE 2012), pp. 142–147, 2012
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Minkowski Gasket Electromagnetic Band Gap Structure for Multiband
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Flexible Sierpinski Carpet Fractal Antenna on a Hilbert Slot Patterned
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issue 4, pp. 1-7, 2012
[E] S. Sadat, M. Fardis, G. Dadashzadeh, R. K. Baee, ProximityCoupled Microstrip Patch Antenna Miniaturization using New Fractal
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Pacific Conference on Applied Electromagnetics (APACE 2007), pp. 16, 2007
Investigation of Minkowski Patch Antenna with
Meander Line Split Ring Resonator (ML-SRR)
Structure
1
H. Nornikman, 1B. H. Ahmad, 1M. Z. A. Abd Aziz, 2M. K. A. Rahim, 1A. R. Othman
1
Center for Telecommunication Research and Innovation (CeTRI),
Faculty of Electronics and Computer Engineering,
Universiti Teknikal Malaysia Melaka (UTeM), Melaka, Malaysia
2
Faculty of Electrical Engineering,
Universiti Teknologi Malaysia, Johor, Malaysia
nornikman84@yahoo.com, badrulhisham@utem.edu.my, mohamadzoinol@utem.edu.my, mkamal@fke.utm.my,
rani@utem.edu.my
Abstract—The objective of this paper is to investigate the
effect of the meander line split ring resonator on the modified
Minkowski patch antenna. In this work, a modified Minkowski
patch antenna with meander line split ring resonator (ML-SRR)
and quadruple-P shaped split ring resonator (QPS-SRR)
structure is presented. This proposed modified patch antenna
with SRRs structures achieved remarkable 2.644 dB of gain at
the frequency of 2.402 GHz compared to the normal Minkowski
antenna without SRR structures with only 2.348 dB. This
antenna had been simulated in the CST Microwave Studio
simulation software.
that four rectangular or square shape of copper had been cut
from the patch, shown in Figure 1.
(a)
Index Terms—Minkowski antenna, split ring resonator,
metamaterial
I.
(b)
INTRODUCTION
In recent years, there are many works to enhance the gain
performance of the patch antenna design. The metamaterial or
left-handed media (LHM) structure is one of the technique
improve this problem. In 1968, Veselago had been proposed
this technique by implementing split ring resonator (SRR)
structure with metal wires [1]. Many researchers have studied
patch antenna that adds this SRR structure, especially in
wireless local area network (WLAN) range of 2.4 GHz. This
paper had been investigating the effect of the meander line split
ring resonator (ML-SRR) and the quadruple-P shaped split ring
resonator (QPS-SRR) structure of the modified Minkowsi
patch antenna. The parameters that are considered in this work
are return loss, gain, directivity, and the radiation pattern of the
patch antenna [2].
The geometry Fractal methods can include in many types
such as Sierpinski carpet [3], Koch Fractal [4], Minkowski
Fractal [5-6] Hilbert Fractal [7] and 3/2 Curve Fractal [8]. The
Minkowski Fractal antenna is one popular technique to
miniaturize the size of the patch antenna [9]. This Minkowski
Fractal also can affect the multiband of frequency [10].
The Minkowski curve can be characterized by the iteration
factor [11]. Zero iteration is represented by the normal patch
without any scraped out of copper [12]. First iteration show
978-88-907018-3-2/13 ©2013 IEEE
(c)
(d)
Figure 1. Modified Minkowski patch antenna iteration stage ; (a) Zero
iteration; (b) First iteration; (c) Second iteration (d) Third iteration
II.
PROPOSED SRR
Split ring resonators (SRRs) design is used to produce the
negative dielectric constant (permittivity) and negative
permeability [13]. From the previous work, this structure can
increase the gain and miniaturize the size of the patch antenna
and have the capability to improve the gain performance [1415]. This SRR structure also has potential to increase the
reflection loss performance of the pyramidal microwave
absorber [16]. Figure 2 and Table I shows the proposed
meander line split ring resonator (ML-SRR) while Figure 3 and
3233
2013 7th European Conference on Antennas and Propagation (EuCAP)
Table II shows the Quadruple-P shaped split ring resonator
(QPS-SRR). The dimension of the ML-SRR is 8.29 mm x
10.33 mm. The dimension of the larger QPS-SRR is 1.68 mm x
2.49 mm while the dimension of the smaller QPS-SRR is 1.37
mm x 2.03 mm.
A1
III.
PROPOSED ANTENNA
Minkowski Fractal shape based antenna is designed based
on the bigger and smaller size of square shape generator [3].
Figure 4 and Table III shows the modified Minkowski patch
antenna (without SRR structure added). This antenna uses FR4 board substrates with dielectric constant of 4.3, tangent loss
of 0.025, and thickness of 1.6 mm .
Ws
Wp
(a)
(b)
A2
Ls
Lp
Figure 2. Structure unit of meander line split ring resonator (ML-SRR) (a)
normal condition SRR; (b) complimentary SRR condition
TABLE I.
Wf
Lf
DIMENSION OF THE STRUCTURE UNIT OF MEANDER LINE SPLIT
RING RESONATOR (ML-SRR)
Parameter part
Dimension (mm)
A1
A2
8.29
Lc
Wc
Figure 4. Modified Minkowski patch antenna (without SRR structure added)
10.33
TABLE III.
C1
Parameter part
Dimension (mm)
Ws
Ls
34
45
Wp
28.86
Lp
28.86
Wf
0.5
Lf
9.95
Lc
4.55
Wc
2.81
C2
B2
(a)
B1
(b)
Figure 3. Quadruple-P shaped split ring resonator (QPS-SRR); B1 = 1.68
mm, B2 = 1.37 mm, C1 = 2.49 mm, C2 = 2.03 mm (a) normal condition SRR;
(b) complimentary SRR condition
TABLE II.
DIMENSION OF THE MODIFIED MINKOWSKI PATCH ANTENNA
(WITHOUT SRR STRUCTURE ADDED)
DIMENSION OF THE STRUCTURE UNIT OF QUADRUPLE-P
SHAPEDSPLIT RING RESONATOR (QPS-SRR)
Parameter part
Dimension (mm)
B1
B2
1.07
C1
1.68
C2
0.76
1.29
Figure 5 shows the different location of ML-SRR and
QPS-SRR structure of the modified Minkowski patch antenna.
Type A antenna had been representing the attached 4 pair of
ML-SRR and QPS-SRR at the patch antenna to improve the
gain performance. In Type B, a rectangular stripline had been
added to control the location of the resonant frequency of the
antenna.
3234
2013 7th European Conference on Antennas and Propagation (EuCAP)
frequency. The best reflection loss had been shown by second
iteration of the Minkowski patch antenna. This antenna had
been resonating at 2.402 GHz of frequency. The third iteration
shows the worst return loss performance but it had been shifted
from 2.402 GHz to the 2.202 GHz, the different frequency
point of 200 MHz.
Return Loss of Modified Minkowski Patch Antenna with SRR
0
Z1
(b)
-10
Return loss, dB
(a)
-20
-30
Zero Iteration
First Iteration
Second Iteration
Third Iteration
-40
-50
Z3
Z2
2.1
2.3
2.4
2.5
2.6
Frequency, GHz
(d)
(c)
Figure 6. Return loss performance of modified Minkowski patch antenna
with ML-SRR and QPS-SRR (in different iteration stage)
Figure 5. Modified Minkowski patch antenna with different variation ;
(a)Type A; (b) Type B; (c) Type C (d) Type D
For the Type C antenna, a larger version of QPS-SRR
antenna had been added at the center location of patch antenna
to enhance more gain of the antenna. In the Type D, 4 smaller
versions of QPS-SRR had been removed from the design.
Table IV shows the adjustment Stripline length to optimize the
resonant frequency to 2.402 GHz
TABLE IV.
2.2
THE ADDITION OF STRIPLINE TO ADJUST THE FREQUENCY
RANGE TO 2.402 GHZ
Table V shows return loss, resonant frequency and the
bandwidth of the Minkowski patch antenna. It shows that the
second iteration Minkowski patch antenna had been achieved
the best reflection loss with - 47.990 dB at a frequency of
2.402 GHz. The worst return loss performance had been
achieved by third iteration by only - 14.665 dB but it has the
wider bandwidth compared to the other iteration stage. This
antenna (at third iteration stage) has a bandwidth of 100.7
MHz.
Minkowski Antenna type
Rectangular strip
length added (mm)
Without SRR
-
Type A
-
Minkowski
Antenna stage
Resonant
frequency
Return loss
(dB)
Bandwidth
(MHz)
Type B
5.2
Zero iteration
2.312
- 22.680
70.7
Type C
6.8
First iteration
2.392
- 36.925
69.6
Second iteration
2.402
- 47.990
60.8
Type D
6.8
Third iteration
2.202
-14.665
100.7
IV.
TABLE V.
RETURN LOSS PERFORMANCE OF MODIFIED MINKOWSKI
PATCH ANTENNA WITH ML-SRR AND QPS-SRR (IN DIFFERENT ITERATION
STAGE)
RESULT
Figure 6 shows the return loss performance of the modified
Minkowski patch antenna with ML-SRR and QPS-SRR (in
different iteration stage). From the graph, it shows that, the
different type of stage will control where is the resonant
Table VI represents the result of the gain and the directivity
of the antenna (in different iteration stage). The first iteration
shown the best gain performance with 2.495 dB while the
worst gain had been shown by third iteration with only 0.775
dB.
3235
2013 7th European Conference on Antennas and Propagation (EuCAP)
TABLE VI.
GAIN AND DIRECTIVITY PERFORMANCE OF MODIFIED
MINKOWSKI PATCH ANTENNA WITH ML-SRR AND QPS-SRR (IN DIFFERENT
ITERATION STAGE)
Minkowski Antenna
iteration stage
Gain (dB)
Directivity (dBi)
Zero iteration
2.332
5.441
First iteration
2.495
5.505
Second iteration
2.348
5.539
Third iteration
0.775
5.434
patch antenna from the 2.348 dB to 2.644 dB. The addition of
the rectangular stripline had been located back the resonant
frequency from the 2.480 GHz at the Type A to 2.402 GHz in
Type B antenna. This SRR structure did not give the big impact
of the bandwidth performance.
Figure 8 shows the 3D radiation pattern of the modified
Minkowski antenna with SRR structure.Table VIII represents
the gain and directivity performance of the different type of
modified Minkowski patch antenna.
Figure 7 and Table VII shows the resonant frequency,
return loss and bandwidth of the different type of modified
Minkowski patch antenna From the graph, it shows that the
best performance of the return loss is the modified Minkowski
patch antenna (without SRR structure) with – 47.999 dB at
2.402 GHz of frequency.
Return Loss of Different Type of
Modified Minkowski Patch Antenna with SRR
10
0
Return loss, dB
-10
-20
-30
-40
Without SRR
Type A
Type B
Type C
Type D
-50
-60
2.30
2.35
2.40
2.45
2.50
2.55
Frequency, GHz
Figure 7. Return loss performance of the different type of modified
Minkowski patch antenna with ML-SRR and QPS-SRR
TABLE VII.
RETURN LOSS AND BANDWIDTH OF DIFFERENT TYPE OF
MINKOWSKI PATCH ANTENNA WITH SRR
Figure 8. 3D radiation pattern of the antenna
Minkowski
Antenna type
Resonant
frequency
Return loss
(dB)
Bandwidth
(MHz)
Without SRR
2.402
- 47.990
69.8
Type A
2.480
- 33.340
72.3
Directivity (dBi)
2.402
- 38.128
68.1
Minkowski Antenna
type
Gain (dB)
Type B
Type C
2.402
- 31.328
68.7
Without SRR
2.348
5.539
Type D
2.402
- 38.086
71.3
Type A
2.627
5.644
Type B
2.644
5.506
Type C
2.629
5.501
Type D
2.486
5.522
TABLE VIII.
The addition of the SRR structure had been reduced the
return loss performance. The addition of the SRR had been
enhanced the gain of the Minkowski patch antenna. It shows
that in Type B antenna, it increases the gain of the Minkowski
3236
GAIN AND DIRECTIVITY OF DIFFERENT TYPE OF MINKOWSKI
PATCH ANTENNA WITH SRR
2013 7th European Conference on Antennas and Propagation (EuCAP)
V.
CONCLUSION
After simulation done, it shows that the gain had been
enhanced by the addition of the ML-SRR and QPS-SRR on the
modified Minkowski patch antenna. An improvement of the
gain by 0.296 dB from 2.348 dB to 2.644 dB. The SRR has the
capability can control the resonant frequency. The proposed
antenna design can be integrated with RF transmitter [17] and
RF receiver [18] to form a complete WLAN front-end system.
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